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http://dx.doi.org/10.29220/CSAM.2018.25.1.091

An optimal continuous type investment policy for the surplus in a risk model  

Choi, Seung Kyoung (Department of Statistics, Sookmyung Women's University)
Lee, Eui Yong (Department of Statistics, Sookmyung Women's University)
Publication Information
Communications for Statistical Applications and Methods / v.25, no.1, 2018 , pp. 91-97 More about this Journal
Abstract
In this paper, we show that there exists an optimal investment policy for the surplus in a risk model, in which the surplus is continuously invested to other business at a constant rate a > 0, whenever the level of the surplus exceeds a given threshold V > 0. We assign, to the risk model, two costs, the penalty per unit time while the level of the surplus being under V > 0 and the opportunity cost per unit time by keeping a unit amount of the surplus. After calculating the long-run average cost per unit time, we show that there exists an optimal investment rate $a^*$>0 which minimizes the long-run average cost per unit time, when the claim amount follows an exponential distribution.
Keywords
risk model; surplus process; continuous type investment policy; long-run average cost; optimal investment rate;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Cho EY, Choi SK, and Lee EY (2013). Transient and stationary analyses of the surplus in a risk model, Communications for Statistical Applications and Methods, 20, 475-480.   DOI
2 Cho YH, Choi SK, and Lee EY (2016). Stationary distribution of the surplus process in a risk model with a continuous type investment, Communications for Statistical Applications and Methods, 23, 423-432.   DOI
3 Dickson DCM and Willmot GE (2005). The density of the time to ruin in the classical Poisson risk model, ASTIN Bulletin, 35, 45-60.   DOI
4 Dufresne F and Gerber HU (1991). Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance: Mathematics and Economics, 10, 51-59.
5 Gerber HU (1990). When does the surplus reach a given target?, Insurance: Mathematics and Economics, 9, 115-119.
6 Gerber HU and Shiu ESW (1997). The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin, Insurance: Mathematics and Economics, 21, 129-137.   DOI
7 Klugman SA, Panjer HH, and Willmot GE (2004). Loss Models: From Data to Decisions (2nd ed), John Wiley & Sons, Hoboken, NJ.
8 Lim SE, Choi SK, and Lee EY (2016). An optimal management policy for the surplus process with investments, The Korean Journal of Applied Statistics, 29, 1165-1172.
9 Ross SM (1996). Stochastic Processes (2nd ed), John Wiley & Sons, New York.